Return samples drawn from a log-normal distribution.
Draw samples from a log-normal distribution with specified mean, standard deviation, and array shape. Note that the mean and standard deviation are not the values for the distribution itself, but of the underlying normal distribution it is derived from.
Parameters : | mean : float
sigma : float, > 0.
size : tuple of ints
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Returns : | samples : ndarray or float
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See also
Notes
A variable x has a log-normal distribution if log(x) is normally distributed. The probability density function for the log-normal distribution is:
where is the mean and
is the standard
deviation of the normally distributed logarithm of the variable.
A log-normal distribution results if a random variable is the product
of a large number of independent, identically-distributed variables in
the same way that a normal distribution results if the variable is the
sum of a large number of independent, identically-distributed
variables.
References
Limpert, E., Stahel, W. A., and Abbt, M., “Log-normal Distributions across the Sciences: Keys and Clues,” BioScience, Vol. 51, No. 5, May, 2001. http://stat.ethz.ch/~stahel/lognormal/bioscience.pdf
Reiss, R.D. and Thomas, M., Statistical Analysis of Extreme Values, Basel: Birkhauser Verlag, 2001, pp. 31-32.
Examples